Design of Waffle Slab (without beams) by Direct Design Method 32
32
B1
C1
B2
C2
(S1)
32 B4
32 B3
C3
C4
(S1)
(S2)
16.5
B5 16
C5
C6
C7
C8 16
32
(S2)
B6
(S2)
(S3)
B7 16
C9
C10
C11
C12 16
32
(S1)
B8
(S2)
(S1)
B9 16.5
B10
B11
C13
B12
C14 16.5
16
C15 16
16
C16 16
16.5
Building Plan
Assume S = (32 + x/2) , Building spans = (S, S, S) by (S, S, S) Building Height = 4@10 = 40 Loads: LL = 40 psf, FF = 20 psf, RW = 20 psf [i.e., (40 + x/2), (20 + x/4), (20 + x/4) psf] Material Properties: f c = 3 ksi, fs = 20 ksi [i.e., f c = (3 + x/20) ksi, fs = (20 + x/4) ksi
Design of Slabs and Ribs Slabs Assuming 10 square pans per slab; i.e., (3.2 3.2 ) c/c and (2.7 2.7 ) clear spans (with 6 ribs) Slab thickness = 2.5
Self weight = 2.5 150/12 = 31.25 psf
Total load on slab, w = 31.25 + 20 + 20 + 40 = 111.25 psf = 0.111 ksf Maximum Moment for an edge-supported (2.7 2.7 ) slab with Support condition Case 2 M(
) max
= 0.045 wL2 = 0.045
0.111
(2.7)2 = 0.0365 k /
Modulus of rupture = 5 fc = 5 (3/1000) = 0.274 ksi; i.e., Allowable tensile stress = 0.274/2 = 0.137 ksi Ssect = bh2/6
0.0365 = h2/6
0.137
hreq = (0.0365
6/0.137) = 1.26
As(Temp) = 0.0025 bh = 0.0025 12 2.5 = 0.075 in2/ft
Slab thickness, h = 2.5 is OK; i.e. d = 2
Use appropriate wire mesh to provide the required As(Temp); i.e., 1/8 -wire diameter (2 2 ) mesh
Ribs Maximum clear span = 31 ; Slab without edge beam and fy = 40 ksi Slab thickness = Ln(0.8 + fy/200)/33 = 31 (0.8 + 40/200) 12/33 = 11.27 Assume 18 thickness; i.e., 13.5 below slab, with bw = 6 Average thickness without column head = 18 {(2.7 If column head covers (5 = 6.97 + {25
(2.7
2.7)
15.5}/(3.2
3.2) = 6.97
5 = 25) square pans, average thickness of slab
2.7)
15.5}/(32
32) = 9.72
Assuming the entire slab thickness to be = 9.72 Self weight = 9.72
150/12 = 121.5 psf
Total load on slab = 121.5 + 20 + 20 + 40
201.5 psf = 0.202 ksf
For design, n = 9, k = 0.378, j = 0.874, R = 0.223 ksi d = 18
1.5 = 16.5 ; As = M/fsjd = M 12/(20 0.874 16.5) = M/24.04
Moment capacity Mc(max) = Rbd2 = 0.223 1 16.52 = 60.70 k / , or 30.35 k /rib Also, As(Temp) = 0.0025 bt = 0.0025 12 18 = 0.54 in2/ ; or 0.27 in2/rib {322 (16 + 2/12)2} = 153.71 k
Punching shear force in slab
0.202
and in column head
{322 (12/12 + 16.5/12)2} = 205.25 k
0.202
Stresses are = 153.71/(4(16
12 + 2) 2) = 0.099 ksi and = 205.25/(4(12 + 16.5) 16.5) = 0.109 ksi
Allowable punching shear stress,
punch
= 2 fc = 2 (3/1000) = 0.110 ksi
OK for punching shear
Panels in the Long and Short Direction Panel 1 (and all other panels) Width of Panel = 16.5 No edge beam along panel length; Also no transverse beam
t
1
= 0, for all slabs
= 0, for all slabs
Column strip = Short span (c/c)/4 = 32/4 = 8 , Middle strip = 16 8 = 8 (i.e., 2.5 pans per strip) Slab (S1) Slab size (= 32 32 c/c) = 31 31 M0 = wL2Ln2/8 = 0.202 16.5 312/8 = 399.48 k Support (c)
MExt = 0.26 M0 = 103.87 k , M+ = 0.52 M0 = 207.73 k , MInt = 0.70 M0 = 279.64 k
L2/L1 = 32/32 = 1.0,
1L2/L1
=0
Total column strip moments are MCExt = 1.00 MExt = 103.87 k ; i.e., 103.87 k /8 = 12.98 k / ; AsCExt = 12.98/24.04 = 0.54 in2/ MC+ = 0.60 M+ = 124.64 k ; i.e., 124.64 k /2.5 rib = 49.86 k / ; ACExt+ = 49.86/24.04 = 2.07 in2/rib MCInt = 0.75 MInt = 209.73 k ; 209.73 k /8 = 26.22 k / ; AsCInt = 26.22/24.04 = 1.09 in2/ Total middle strip moments are MMExt = 103.87 103.87 = 0 k ; i.e., 0 k /8 = 0 k / ; AsMExt = 0/24.04 = 0.0 in2/ MM+ = 207.73 124.64 = 83.09 k ; i.e., 83.09 k /2.5 rib = 33.24 k /rib; AM+ = 33.24/24.04 = 1.38 in2/rib MMInt = 279.64 209.73 = 69.91 k ; i.e., 69.91 k /8 = 8.74 k / ; AMInt+ = 8.74/24.04 = 0.36 in2/
Slab (S2) Slab size (= 32 32 c/c) = 31 31 M0 = wL2Ln2/8 = 0.202 16.5 312/8 = 399.48 k Interior Support
MInt = 0.65 M0 = 259.67 k , M+ = 0.35 M0 = 139.82 k , MInt = 0.65 M0 = 259.67 k
L2/L1 = 32/32 = 1.0,
1L2/L1
=0
Total column strip moments are MCInt = 0.75 MExt = 194.75 k ; i.e., 194.75 k /8 = 24.34 k / ; AsCInt = 24.34/24.04 = 1.01 in2/ MC+ = 0.60 M+ = 83.89 k ; i.e., 83.89 k /2.5 rib = 33.56 k /rib; AsM+ = 33.56/24.04 = 1.40 in2/rib MCInt = 0.75 MInt = 194.75 k ; i.e., 194.75 k /8 = 24.34 k / ; AsCInt = 24.34/24.04 = 1.01 in2/ Total middle strip moments are MMInt = 259.67 194.75 = 64.92 k ; i.e., 64.92 k /8 = 8.11 k / ; AsMInt = 8.11/24.04 = 0.34 in2/ MM+ = 139.82 83.89 = 55.93 k ; i.e., 55.93 k /2.5 rib = 22.37 k /rib; AsM+ = 22.37/24.04 = 0.93 in2/rib MMInt = 259.67 194.75 = 64.92 k ; i.e., 64.92 k /8 = 8.11 k / ; AsMInt = 8.11/24.04 = 0.34 in2/
Denoting slab reinforcement by in2/ ( ve) and rib reinforcement by in2/rib (+ve highlighted)
0.54
2.07
1.09
1.01
1.40
1.01
1.09
2.07
0.54
0.00
1.38
0.36
0.34
0.93
0.34
0.36
1.38
0.00
0.54
2.07
1.09
1.01
1.40
1.01
1.09
2.07
0.54
0.54
2.07
1.09
1.01
1.40
1.01
1.09
2.07
0.54
0.00
1.38
0.36
0.34
0.93
0.34
0.36
1.38
0.00
0.54
2.07
1.09
1.01
1.40
1.01
1.09
2.07
0.54
0.54
2.07
1.09
1.01
1.40
1.01
1.09
2.07
0.54
0.00
1.38
0.36
0.34
0.93
0.34
0.36
1.38
0.00
0.54
2.07
1.09
1.01
1.40
1.01
1.09
2.07
0.54
1 #4 extra top between alternate #4 bars
#4 @ 4.5 c/c within slab A
B
3.2
#4@ 4.5 c/c
A
B
2 #9 through
2 #9 Section A-A
Ribs within Column Strip
3.2
#4 @ 7.5 c/c
#4@ 4.5 c/c + extra top Section B-B
2 #8 through
Ribs within Middle Strip
2 #9
